aircraft wake vortices: physics and ucl...

Aircraft wake vortices: physics and UCL models

Institute of Mechanics, Materials and Civil Engineering (iMMC)Ecole Polytechnique de Louvain (EPL)Université catholique de Louvain (UCL)1348 Louvain-la-Neuve, [email protected]

G. Winckelmans

WakeNet3-Europe Specific Workshop« RE-CATEGORIZATION »TU Berlin, Germany, June 20-21, 2011

Developed wakes, shortly after rollup

Developed wakes, shortly after rollup

2VS IGE generated close to the ground and with weak cross wind

Simulation by L. Bricteux et al. (UCL)work with Airbus on further investigations of WV IGE, after UCL work in FAR-Wake

Longitudinally averaged flow

Longitudinally averaged flow

Circulation decay (RECAT I model also shown)

no wind, no initial turbulence

weak crosswind, upwind vortex

weak crosswind, downwind vortex

Iso-2 surfaces colored by the axial vorticity

2VS OGE and without Crow instabilities

Cases with same initial circulation but different core sizes: thus energyand induced drag are different. Source: De Visscher et al. (UCL)

Case 1:

Case 2:

For each case, the curve presents the average of the core radius measurements. Those were measured in each cross-plane, and “sitting” on each local vortex center (port and starboard)

Time evolution of the core radius:

2VS with Crow instability

Case N*=0 and weak turbulence

Source: De Visscher et al. (UCL), submitted

Iso-2 surfaces colored by the axial vorticity

Case with stratification

Case N*=0.35 and weak turbulence

Comparison of the longitudinally-averaged circulation evolution

Comparison of the mean and 95%-envelope circulation evolution

Improved circulation decay modelingStratification effect Stratification and turbulence effects

Improved vortex transport modeling

WAKE4D: “3-D space + time” wake vortex prediction platform

• It uses as input:

– the a/c trajectory

– the met conditions.

• The computational domain is divided in various “computational gates” crossing the flight path.

• The aircraft crossing one of the gates generates a pair of wake vortices (WV) that are transported (also by the headwind) and also decay.

The Deterministic wake Vortex Model (DVM)

• The DVM forecasts, in real-time, the WV behavior (transport and decay) in one computational gate, using simplified physical models.

• The initial wake is computed using the a/c characteristics (position, mass, TAS, wingspan, lift distribution, and flight angles) when the aircraft crosses the gate.

• Each primary wake vortex is represented by a vortex particle with a chosen circulation distribution profile:

– Burnham-Hallock model (= low-order algebraic model),

– high-order algebraic model, or

– two-scales Proctor-Winckelmans model

• Alternative: wake vortex sheet model discretized using small vortex particles

23

“One-scale” models for each vortex of the 2VS

• Definitions :

“One-scale” models for each vortex of the 2VS

GaussianHOALOA (BH)Top hat

• e.g., Jacquin, Proctor-Winckelmans

• Proctor-Winckelmans model:

with , , and determined by

“Two-scales” models for each vortex of the 2VS

• Two-scales models are superior in term of azimuthal velocity and circulation profiles (here calibration from space-developing simulation of WV rollup)

Jackson et al., TP 13629E, 2001 de Bruin and Winckelmans, AW-114-25, Awiator, 2005 Lonfils et al., TR1.1.2-6, Far-Wake, 2008

Circulations: versus • The WV total circulation 0 is greater than the “Lidar processed” WV

circulation 5-15.

• Model of the initial ratio 0 / 5-15 as a function of the wingspan b:

Source: UCL presentation at WN3E 1st major workshop

Vortex sheet model for Near-Field WVE analysis (also collaboration with TUB and with FAA/DLR)

• Parametric model taking into account :

• the tip vortex, • the outer flap vortex, and possibly• the HTP vortex

• The roll-up is calculated using the DVM with several particles

• A routine calculating the near-wake induced velocity field was also developed and used by FAA/DLR

The physical transport models used in the DVM

• Self-induced velocity: Biot-Savart law also using image particles (for NGE modeling)

vu

• Wind convection: by both the axial and lateral components evaluated at the altitude of WV evolution

z

• Stratification effects: the stratification level, N*, is computed from the temperature profile and the thermally induced rebound is modeled

z

v

• Wind shear: the shear of the wind profile is computed and the tilting effect is modeled

y

z

The physical models used in the DVM

• Circulation decay– Two phase decay: slow decay phase followed by a rapid decay phase

– Accumulated “time-to-demise” approach: starting time of the fast decay phase td(EDR, N*)

– The decay rate of both phases also depends on EDR and N*

– Possibility to also use a TKE-based decay model or the APA decay model using EDR

• Crow instability model– Model of the space developing Crow instability amplitude for predicting the WV deformation

– Based on the time-to-demise and thus the atmosphere turbulence level

30

Velocity field evaluation module: case using WAKE4D results with Crow instability effects (case with significant atm turbulence)

aircraft

Zone where the Crow instability is not developed yetZone where the Crow

instability is almost at reconnection

Source: UCL presentation at WN3E specific workshop at TUB

Application of DVM to relative comparison of a/c OGE

Variation of weight, wingspan for constant met. conditions : no wind, turbulence ( ) and no stratification

Example where same loading factor was assumed for both aircraft:

Source: UCL presentation at WN3E 1st major workshop

DVM In Ground Effect (IGE) modeling

• Generate new « secondary » vortex particles close to the ground, to model the ground-generated boundary layer due to no-slip

• Those particles also dynamically separate from the ground

• They interact with the primary vortices and induce the rebound

• There is a redistribution of the secondary particles when the primary vortex has bounced

• An additional IGE decay model, based on a “Particle strength exchange”, enhances the decay of the vortices IGE after rebound.

Comparison between LES and DVM results: case IGE with headwind (from FAR-Wake)

Mean axial vorticity field as computed by a LES Particles used in the DVM to model WV IGE

The Probabilistic wake Vortex Model (PVM)

• Probabilistic modeling and assessment of wake vortices is operationally required.

• The PVM is an upper software layer, based on a Monte-Carlo approach, using the DVM as a subtool.

• For each PVM run, many DVM runs are performed, with random variations on the impact parameters (each one following its own distribution):

– met conditions (natural variations and uncertainties)

– a/c characteristics (uncertainties)

– some coefficients of the physical models (calibration uncertainties)

PVM outputs

• One then obtains, in a computational gate at each time:

– a set of vortex positions,

– their associated circulations.

• Thus: the output distribution is not just a simple image of the input distribution

• A statistical analysis on the result sample can be performed to obtain:

– PDF, mean, median, variance, percentiles, …

Solid : medianDash : 95 % envelopes

Bootstrap resampling technique

• Aim : obtain conservative statistical results while limiting the number of DVM runs

• The resampling technique provides an estimate of the variance of the statistics of the Monte-Carlo results

• The “statistics on the statistics” converge fast

=> PVM confidence envelopes are accurate using a moderate number of DVM runs.

• Thus: the PVM approach is computationally efficient, also for real-time systems.

WAKE4D-DVM and WAKE4D-PVM

• The platform can be run deterministically (using the DVM in each gate) or probabilistically (using the PVM in each gate).

• From the 3-D “gate by gate” DVM (resp. PVM) computations, one can rebuild the 3-D wake (resp. envelope of the wake).

• “Control gate”: interpolation in a fixed plane (similar to a LIDAR scanning plane).

• “Control box”: recording of the vortices present in a box as a function of time.

Visualization of the velocity field (velocity norm, also including the wind field part), as predicted in each

computational gate using the WAKE4D-DVM

aircraftControl gate

Computational gate

iMMC 38

• Met. conditions :– Southern wind profile (log profile)– Turbulence (EDR=10-4 m2/s3 OGE,

then log law)– No stratification

Example of use of WAKE4D : approach to Marseille-Provence

•Aircraft : B747- 400

–MLW : 285,000 kg

–b=64.4 m

–s= 0.75 [-]

iMMC 39

Aircraft trajectory

x

yz

• The proper trajectory corresponding to the ac characteristics and the wind is calculated using a WAKE4D “pre-processor” tool

iMMC 40

Computational gate locations

• 144 computational gates with 2.5 s between two gates

• Here we use the WAKE4D-DVM

Rolling moment induced by a 2VS on a followeraircraft

• Induced rolling moment:

Further assumptions

• Wing with uniform lift slope:

• Wing with linear taper:

• Remove the non-contribution of the fuselage of diameter

• One then obtains:

• For simplicity, we here assume that each longitudinally averagedvortex is well represented by a low order algebraic (LOA = B-H) circulation profile:

• The induced azimuthal velocity due to one vortex is then:

• The other models could be investigated as well (not done yet)

Model used so far in simplified analysis

• Case :

• One then obtains:

• All other cases can be analyzed as well: this was done

Case with wing fully to the left of the left (port) vortex center: contribution of that vortex

B747-400 leader

A380-800 leader

Exemple with A320 follower (medium)

Relative comparisons

• Compute the following dimensionless quantities:– a/c encountering the wake of a/c 1 (B747-400):

– a/c encountering the wake of a/c 2 (A380-800):

• Assume a ratio for the circulations:

• Hence:Plots to be compared!

A320 follower, wrt 2VS center:

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

dc/b

G1, β

G2

A320 follower, wrt 2VS center

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

dc/b

G1, β

G2


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

dc/b

G1, β

G2


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

dc/b

G1, β

G2

Conclusion of simplified static analysis

• Static analysis of rolling moment induced by 2VS (i.e., before Crow instabilities)

• Leaders: A380-800 and B747-400, with same rc/b0

• Followers: A320 and A300B2• Even when assuming 25% more circulation for the A380-800 (which is

really an upper bound):– the rolling moment when the outer part of the wing is within one

vortex core (i.e., case d/b=0.5) is « much the same ». This iseven more so when using more realistic values of b0/b.

– The rolling moment when the a/c center is inside one vortex core(i.e., case d/b=0) is still higher, yet by less than 25%. This is evenmore so when using more realistic values of b0/b.

• Hence: circulation is not the whole story: there is also rc ; and b0/b.

aircraft wake vortices: physics and ucl...

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